A341730 Maximum number of sides in any cell in a regular 2n-gon with all diagonals drawn (cf. A007678).

3, 4, 4, 5, 4, 5, 6, 7, 8, 8, 6, 8, 8, 6, 7, 8, 8, 8, 12, 8, 10, 8, 10, 10, 8, 10, 10, 10, 9, 10, 10, 9, 10, 10, 10, 10, 12, 10, 10, 10, 10, 10, 10, 10, 14, 10, 10, 10, 10, 12, 12, 10, 11, 10, 12, 10, 12, 12, 14, 14, 12, 12, 12, 12, 14, 12, 12

Offset

2,1

Comments

A bisection of A341729.

a(46) = 14, corresponding to a regular 92-gon, suggesting that this sequence may be unbounded (cf. A342222). (The Pfetsch-Ziegler web page discusses a similar question for polygons defined by grid points.) It would be nice to have a b-file.

For which values of n is a(n) odd (and why)?

Links

Table of n, a(n) for n=2..68.

M. E. Pfetsch and G. M. Ziegler, Large chambers in a lattice polygon, December 13, 2004;

M. E. Pfetsch and G. M. Ziegler, Large chambers in a lattice polygon [Local copy of webpage, pdf only]

Crossrefs

Cf. A007678, A062361, A331450, A331451, A341729, A342222.

Sequence in context: A028949 A201006 A107574 * A241163 A053405 A133196

Adjacent sequences: A341727 A341728 A341729 * A341731 A341732 A341733

Keyword

nonn

Author

Scott R. Shannon and N. J. A. Sloane, Mar 06 2021

Status

approved